Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{rm{BSE}}(Delta(A))$ consisting of all  BSE-functions on $Delta(A)$ where $Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterizatio...

Abstract An improved genetic algorithm is proposed to solve the traveling salesman problem. On basis of traditional algorithm, greedy introduced initialize population. The parameters are adjusted adaptively from two aspects evolution algebra and individual fitness function value, which can speed up optimization prevent falling into local optimum. In mutation operation, adaptive used select oper...

Segal’s chronometry is based on a space–time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). There are exactly two more non-commutative four-dimensional Lie algebras that admit such a form. They determine space–times L and F. The world F is based on the Lie algebra u(1,1), in terms of which the pseudo-Hermitian rea...

A scheme to perform the Cartan decomposition for the Lie algebra su(N) of arbitrary finite dimensions is introduced. The scheme is based on two algebraic structures, the conjugate partition and the quotient algebra, that are easily generated by a Cartan subalgebra and generally exist in su(N). In particular, the Lie algebras su(2) and every su(2 < N < 2p) share the isomorphic structure of the q...

In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate  and $ (tau,sigma)$-Boolean  in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary  and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

Adaptability evaluation of software systems is one of the key concerns in both software engineering and requirements engineering. In this paper, we present a formal and systematic approach to evaluate adaptability of software systems to requirements in enterprise business applications. Our approach consists of three major parts, that is, the common modeling method for both business realms and s...

For a time-dependent harmonic oscillator with an inverse squared singular term, we find the generalized invariant using the Lie algebra of SU(2) and construct the number-type eigenstates and the coherent states using the spectrum-generating Lie algebra of SU(1, 1). We obtain the evolution operator in both of the Lie algebras. The number-type eigenstates and the coherent states are constructed g...

We discuss a model of gravity with conformal symmetry appearing in the simplest extension General Relativity Poincar\'e algebra terms. The nonlinear realization causes existence five scalar fields. Therefore it looks desirable to use them for driving inflation at earliest stages Universe evolution. It is shown that evolution scale factor doesn't imply accelerated expansion so there are no infla...